Hi,
I'm not sure what is the problem.
I would surely recommend updating, but I'm not sure it would help.
I do see several javascript errors in the console of the browser on the checkout.
These are caused by some optimization tool moving the javascript files and code in the header at the end of the body, resulting in the javascript directly in the middle of the body not finding what should be already loaded.
I would recommend disabling this so that the javascript is properly added to the head of the pages. That might be enough to fix the problem.
If not, the next step would be trying with the default template of Joomla, to see if it is linked to a view override, or some problem in the template, and if you have the problem even with the default template, then updating should be the solution.
The frontend of HikaShop on your website looks fairly normal so I don't expect much issue with the update of HikaShop. I think it will do more good than bad.